a) Field of the invention
The present invention relates to an objective optical system for endoscopes such as fiber scopes and non-flexible endoscopes.
b) Description of the prior art
It is demanded for objective lens systems for endoscopes to satisfy the telecentric condition in order to avoid problems such as degradation of transmission efficiency of the offaxial rays through image guides in fiber scopes, degradation of transmission efficiency of the offaxial rays through relay optical systems in non-flexible endoscopes and production of the color shading in video scopes using image pickup devices. Remarkable distortion is produced in the objective lens systems which satisfy the telecentric condition.
Distortion in optical systems is dependent on angle of incidence .theta..sub.1 of the principal ray on the entrance pupil.
When image height by H(.theta..sub.1), distortion D(.theta..sub.1) is defined by the following formula (i): ##EQU1## wherein the reference symbol f represents the focal length of the objective optical system of interest.
Though image height H(.theta..sub.1) is dependent on both the focal length and angle of incidence .theta..sub.1, it is generally expressed as a product of the focal length f multiplied by a function of .theta..sub.1, i.e., in a form of H(.theta..sub.1) =fA(.theta..sub.1), taking A(.theta..sub.1) as a proper function of .theta..sub.1. When this equation is used in the above-mentioned formula (i), it is transformed into the following formula (ii) ##EQU2##
Since the relationship between distortion D(.theta..sub.1) and the angle of incidence .theta..sub.1 of the principal ray is determined simply by the function representing the relationship between the image height H(.theta..sub.1) and angle of incidence .theta..sub.1, the function A(.theta..sub.1) represents the distortion in the optical system of interest.
The function A(.theta..sub.1) is generally dependent only on imaged condition of pupil, and this dependency is classified into dependency on the paraxial magnification and dependency on aberrations of image of pupil (offence degree of the sine condition and spherical aberration when the pupil is considered as an object point). When the optical system is free from the aberrations of pupil, i.e., on an assumption that the sine condition of pupil is satisfied at all image heights in the objective optical system, and the spherical aberration of pupil is not produced neigher at the entrance pupil nor the exit pupil, A(.theta..sub.1) is determined uniquely by using the paraxial magnification of pupil .beta..sub.E of the entire optical system as a parameter. That is to say, A(.theta..sub.1) is given by the following formula (iii): ##EQU3##
In order to satisfy the telecentric condition, it is necessary to reserve a sufficiently large absolute value .vertline..beta..sub.E .vertline. for the paraxial magnification of an objective lens system for endoscopes.
When .vertline..beta..sub.E .vertline. has a sufficiently large value, it is possible from the formula (iii) to approximate A(.theta..sub.1) as follows: EQU A(.theta..sub.1).apprxeq. sin .theta..sub.1
Hence, it is possible from the formula (iii) to express distortion D(.theta..sub.1) as follows: EQU D(.theta..sub.1).apprxeq.100.times.(cos .theta..sub.1 -1) (%)
It is understood from this formula that negative distortion is aggravated as .theta..sub.1 increases.
In an objective lens system for endoscopes which must satisfy the telecentric condition as described above, remarkable distortion is produced due to the paraxial magnification of pupil. In order to correct this distortion, it is necessary to forcibly increase the offence degree of the sine condition remarkably for the image of pupil.
As is understood from the foregoing description, the correction of distortion in an objective lens system for endoscopes is characterized in that it requires forcible production of a specific type of aberration. When the specific type of aberration which is not produced ordinarily in an objective lens system for endoscopes is forcibly produced, there will result in difficulty in correction of the other types of aberrations.
When offence degree of the sine condition of image of pupil is increased for correcting distortion in an optical system for endoscopes, the asymmetrical aberrations, i.e., astigmatism and coma, are influenced directly. Further, when an attempt is made to design a compact wide-angle objective optical system, it will become difficult to correct aberrations, especially the offaxial aberrations. Therefore, correction of aberrations other than distortion is the key point in designing an objective optical system for endoscopes when it has a wide angle, sufficiently corrected distortion and a compact size (especially a small outside diameter).
The objective optical system disclosed by Japanese Patent Kokai Publication No. 61-169818 consists of a front lens group and a rear lens group which are arranged on both sides of a stop, comprises at least one aspherical surface in the front lens group, is designed as a telecentric system and has corrected distortion. However, this conventional objective optical system is not compact.
Further, the optical system disclosed by Japanese Patent Kokai Publication No. 61-162021 consists of a front lens group and a rear lens group which are arranged on both sides of a stop, comprises at least one aspherical surface in each of the lens groups, and has distortion and astigmatism corrected at the same time. Speaking more concretely, this objective optical system corrects astigmatism by utilizing the reverse signs of astigmatism coefficients which are selected for the aspherical surface used in the front lens group for correcting distortion and the aspherical surface used for in the rear lens group correcting distortion. From the viewpoint of practical use, the embodiment described in the specification of this conventional example has the following problems:
(i) The curve illustrating distortion has an unnatural shape. PA1 (ii) The image surfaces, especially the meridional image surface, have high curvature and remarkable condulations are produced at intermediate image heights on the curves illustrating astigmatism. Accordingly, it cannot be said that the image surface is sufficiently flat over the entire range of the visual field of the optical system. PA1 (iii) The lens system has a diameter which is large as compared with the image height, thereby making it impossible to design the optical system compact. PA1 (iv) The aspherical surfaces have a shape wherein an inflection point is located within an effective diameter, thereby making it difficult to machine a die for molding the lens elements with high precision. PA1 (v) The optical system has a narrow visual field. PA1 wherein the reference symbol f.sub.a represents focal length of the negative meniscus lens element which is designed as the aspherical lens element.
In an objective optical system for endoscopes having a wide angle, distortion may not be corrected sufficiently and it is obliged to allow more or less distortion to remain in the optical system. When the curve illustrating this residual distortion has a shape similar to that of the distortion produced in the conventional objective optical systems, i.e., distortion of the type expressed by the formula D(.theta..sub.1)=100.times.(cos .theta..sub.1 -1) (%), an objective lens system having the above-mentioned residual distortion will give no unnatural impression even to the users accustomed to observation through endoscopes equipped with the objective lens systems having uncorrected distortion. When a distortion curve varies abruptly at large image heights or has local extreme values at intermediate image heights, however, magnification varies unnaturally dependently on image height, thereby giving unnatural impression during observation. Accordingly, it is necessary to solve (i) out of the problems mentioned above.
Distortion in a telecentric optical system such as an objective optical system for endoscopes is corrected in a way different from that for correcting distortion in an ordinary objective optical system as already described above. Speaking concretely, the correction of distortion in a telecentric optical system requires production of a specific type of aberration, for example, remarkable offence of the sine condition. In order to produce the above-mentioned aberration by using aspherical surfaces, it is obliged to select an abnormally larger departure from the reference sphere for the aspherical surfaces than that for the aspherical surfaces used in other types of optical systems. Since it is additionally required to control shapes of distortion curve and astigmatism curve, the aspherical surfaces to be used in a telecentric optical system are obliged in most case to have a shape wherein the aspherical surfaces have inflection points within the effective diameters thereof. Under the current circumstance of the die machining technique, it is difficult to manufacture dies for molding aspherical lenses having such an aspherical surface shape with surface precision high enough for use in observation systems. Accordingly, even when aspherical lenses are usable in objective optical systems from viewpoint of design, it is practically difficult to manufacture such lenses or impossible to manufacture such lenses with high surface precision. It is therefore required to solve (iv) out of the above-mentioned problems.